Methods of Increasing String Efficiency

Methods of Increasing String Efficiency

AU : May-06, 09, 10,11, 13,16, Dec.-14,15

We have seen that higher the value of the string, efficiency, more uniform is the potential distribution over a string of suspension insulators. The line unit is always under the maximum electrical stress. To avoid possibility of puncture of line unit due to excessive stress, efforts are made to have uniform potential distribution. Hence some methods are used in practice to get higher string efficiency. These methods are,

1. Reducing ratio of shunt capacitance to self capacitance

2. By grading the insulators

3. Use of guard ring to provide static shielding

Let us discuss these methods.

 

1. Reducing Ratio of Shunt Capacitance to Self Capacitance

The voltage across the line unit depends on the value of k which is the ratio of shunt capacitance to self capacitance. The string efficiency is dependent on the voltage across the line unit. Lesser the value of k, higher is the string efficiency and more uniform is the potential distribution. The voltages across the various units of string are almost equal for very low values of k.

Now k = C₁/C i.e. the ratio of shunt capacitance to self capacitance. So to reduce the value of k, Q must be reduced. This is possible by increasing the distance between the insulator and the earth i.e. tower. This can be achieved by increasing the length of cross-arms as shown in the Fig. 5.6.1. More the length d of the cross-arm, less is the value of C₁ and less is the value of k.

But this method has practical limitations such as :

1. Use of long cross-arm increases the cost.

2. Due to long cross-arm overall strength of the tower reduces.

Hence in practice, the minimum value k which can be achieved by this method is 0.1. And due to these limitations, this method is rarely used in practice.

 

2. Grading the Insulators

By correct grading of the insulators, more uniform voltage distribution across the string can be achieved. In the method of grading, the insulators are so selected that the self capacitances i.e. mutual capacitance of the various units are different and the values of mutual capacitances decrease from line unit towards top unit. So top unit has minimum mutual capacitance while the line unit has maximum mutual capacitance. The voltage for the given current across the capacitance is inversely proportional to the capacitance. So more the capacitance, lesser is the voltage across the capacitance.

Thus keeping line unit capacitance to be maximum, current through it is minimum. This reduces the voltage across the line unit.

So by properly grading the insulators i.e. by using different sized insulators in a string, uniform voltage distribution can be achieved and string efficiency can be improved. The grading is shown in the Fig. 5.6.3.

The design of such string using different sized insulators is practically complicated and inconvenient. Hence method is used only for very high  voltage system such as 200 kV and above. Though the design of such string is inconvenient, using standard insulators for most of the units and larger units adjacent to the line conductor, better results can be obtained.

 

3. Use of Guard Ring (Static Shielding)

In this method a large metal ring surrounding the line unit and connected to the metal part of the bottom of the line unit is used. Such a ring is called "guard ring". The guard ring is shown in the Fig. 5.6.3. This is also called static shielding of the string.

Earlier it has been mentioned that capacitance between insulator and the line is neglected. But use of guard ring increases the capacitance between the metal part of insulator and the line.

These capacitances are shown as C₂, C₃ in the Fig. 5.6.3. These capacitances are greater for the lower units. Due to this, voltage across these units is reduced. An equal distribution of voltage is not possible by this method.

But the guard ring used can be designed in such a way that shunt capacitance current I_1, I₂, I₃ etc. are equal to the currents through newly introduced capacitors i.e. i₁ , i₂, i₃ etc. as shown in the Fig. 5.6.3. Due to this, charging current through the mutual capacitors remains same, giving uniform voltage distribution. But such a design is practically difficult.

Thus the primary aim of the guard ring is to reduce the electrical stress on the lower units. 

 

Example 5.6.1 A string of 5 suspension insulators is to be graded to obtain uniform distribution of voltage across the string. If the pin to earth capacitances are all equal to C and the mutual capacitance of the top unit is 12 C, find the mutual capacitance of each unit in terms of C.

 Solution :

The arrangement is shown in the Fig. 5.6.4.

Let the mutual capacitances be C₁, C₂, C₃, /// C₄ and C₅.

C₁ = 12 C... Given

The voltage distribution is uniform so voltage across each unit is same as V.

Applying Kirchhoff's current law at node P,

Note that the voltage across shunt capacitance carrying current i₃ is

 V + V + V = 3 V.

Thus the grading is 12 C, 13 C, 15 C, 18 C and 22 C from top to bottom.

 

Example 5.6.2 Each of the three insulators forming a string has a self capacitance of C Farad. The shunting capacitance between earth and metal work of each insulator is 0.18 C while it is 0.1 C between metal work and line. Calculate the voltage across each insulator as a percentage of the line conductor voltage to earth and the string efficiency.

Now a guard ring is provided, increasing the capacitance to the line of the metal work of the lowest unit to 0.25 C. Calculate the new string efficiency and redistribution of the voltage.

Solution : The arrangement without a guard ring is shown in the Fig. 5.6.5.

Note that voltage across C2 carrying current i₁ is the potential of point P with respect to line conductor which is V₂ + V₃.

The voltage across C₁, carrying current i₂ is V₁ + V₂ while voltage across C₂ carrying current i₂ is V₃ alone. 

With a guard ring : The capacitance C2 between metal work of last unit and line i.e. at node Q increases to 0.25 C from 0.1 C due to guard ring.

The equation at node P remains same as,

As the string efficiency is high due to guard ring, there is much more uniform voltage distribution.

Note that the direction of current through C₂ is assumed from right to left, towards the nodes P and Q as the line conductor is always at higher voltage with respect to the nodes.

 

Example 5.6.3 In a transmission line, each conductor is at 20 kV and is supported by a string of 3 suspension insulators. The air capacitance between each cap-pin junction and tower is one fifth of the capacitance of each insulator unit. A guard ring, effective only over the line-end insulator unit is fitted, so that the voltages on 2 units nearest the line end are equal. Calculate

i) The voltage on the line end unit.

ii) The value of capacitance required between the line and the pin.

Solution : The arrangement is shown in the Fig. 5.6.6.

The C_x is connected so that V₂ = V₃.

The insulator currents are I₂ I₂ and I₃ while the charging currents from insulators to earth are I_C1 and I_C2. The guard ring current is lx- As voltage across the insulators are V₁ V₂ and V₃,

 

Example 5.6.4 A string of n suspension insulators is to be fitted with a guard ring. If the pin to earth capacitances are all equal to C, derive the general expression for the line to pin capacitor interms of n, C and P where P is number of pin, so as to give uniform voltage distribution over the string.

If there are 8 suspension insulators, using the expression derived, obtain the values of all line to pin capacitances.

AU : May-06, Marks 16

Solution : The arrangement is shown in the Fig. 5.6.7.

Let all the pin to earth capacitances be C and all the mutual capacitances be C'.

The voltage distribution is uniform hence voltage across each unit is V and the total voltage across the string is nV.

Let C_P1, C_P2, C_P3 ... be the pin to line capacitances existing due to guard ring.

As the voltage distribution is uniform, the charging current through all the mutual capacitances must be same.

Now voltage V_x across the capacitor C_P1 is voltage of node P with respect to line i.e. nV-V = (n-l)V.

Now voltage across C carrying current i₂ is V + V = 2V while voltage across C_P2 is voltage of node Q with respect to line i.e. nV - 2V = (n - 2) V.

Where 2 is number of pin of which C_p2 is the capacitor with line.

Similarly applying KCL at various nodes we can write the expressions for C_P3, C_P4 ... etc.

Looking at the expressions (2) and (4), the general expression for the pin to line capacitance of pth pin is,

C_PP = PC / (n-P) where C_PP = pin to line capacitance of pth pin

P = Number of pin

n = Number of units,

C = Shunt capacitance

Now for n = 8, the values of pin to line capacitances can be obtained as,

 

When there are n units, there are (n - 1) pin to line capacitances exist.

 

Example 5.6.5 Calculate string efficiency for a string of three insulator units if the capacitance of each unit to earth and line he 20 % and 5 % of the self capacitance of the unit. Also obtain voltage distribution.

Solution : The arrangement is shown in the Fig. 5.6.8.

The voltage across C₂ carrying current i₁ is the potential of P with respect to line conductor which is V₂ + V₃. 

 

Example 5.6.6 A 3 unit insulator string is fitted with a guard ring. The capacitances of the link pins to metal work and guard ring can be assumed to be a 15 % and 5 % of the capacitance of each unit. Determine.

1) Voltage distribution 2) String efficiency

Solution : Refer example 5.6.5 for the procedure and verify the answer as :

 i) Voltage distribution is :

V₁ = 30.208 % of V, V₂ = 31.2495 % of V, V₃ = 38.542 % of V and ii) String efficiency = 86.48 %.

 

Example 5.6.7 Each line of a 3-phase system is suspended by a string of three identical insulators of self-capacitance C farad. The shunt capacitance of connecting metal work of each insulator is 0.2 C to earth and 0.1 C to line. Calculate the string efficiency of the system if a guard ring increases the capacitance to the line of metal work of the lowest insulator to 0.3 C.

Solution : The arrangement is shown in the Fig. 5.6.9. The guard ring is used. The current distribution is also shown in the Fig. 5.6.9.

At node P,

 

Example 5.6.8 A string of eight suspension insulators is to be graded to obtain uniform distribution of voltage across the string. If the capacitance of the top unit is 10 times the capacitance to ground of each unit, determine the capacitance of the remaining seven units.

AU : Dec.-15, Marks 10

Solution : The string is shown in the Fig. 5.6.10 Let the mutual capacitances are C₁, C₂,C₃,C₄,C₅,C₆,C₇ and C₈.

C₁ = 10 C  .... given

As voltage distribution is uniform the voltage across each unit is V. Apply Kirchhoff's current law at P,

Note that the voltage across shunt capacitance carrying current i₂ is V + V = 2 V.

Thus the capacitances of remaining seven units are,

11 C, 13 C, 16 C, 20 C, 25 C, 31 C and 38 C.

Review Questions

1. Explain briefly the different methods for improving the string efficiency of an insulator string.

AU : May-11, 16, Marks 8

2. Why guard ring improves the string efficiency ?

3. Explain the role of static shielding in insulators.

4. Each of the three insulators forming a string has self capacitance of C Farad. The shunt capacitance 0/ each metal pin with earth is 0.2 C. While the capacitance of each pin to line is 0.1 C. Calculate the voltage across each insulator as a percentage of the line voltage to earth and the string efficiency.

If now a guard ring is provided, increasing the capacitance to the line of the metal work of the lowest unit to 0.3 C, calculate the new string efficiency and the new distribution 0/ the voltage.

[Ans.: 38.65 %, 30 %, 31 % from bottom to top, 86.2 % without guard ring and 35 %, 32 %, 32.6 % from bottom to top, 95.39% with guard ring]

5. A string of 6 suspension insulators is to be graded to obtain uniform distribution of voltage across the string. If the pin to earth capacitances are all equal to C and the mutual capacitance of the top insulator is 10C, find the mutual capacitance of each unit interms of C.

[Ans.: 10 C, 11C, 13 C, 16 C, 20 C and 25 C]